Suppose you group all the stocks in the world into mutually exclusive portfolios $($each stock is in only one portfolio$)$:

growth stocks and value stocks. Suppose the two portfolios have equal size $($in terms of total value$),$ a correlation of $0\mathrm{.}5,$

and the following characteristics:

$.$ The risk free$-$rate is $4\%.$

a$.$ What is the expected return and volatility of the market portfolio $($which is a $50-50$ combination of the two portfolios$)?$

b$.$ Calculate the Sharpe ratios of the value stock, growth stock, and market portfolio.

c$.$ Does the CAPM hold in this economy? $($Hint: Is the market portfolio efficient?$)$

Data table

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